There are various types of signal processing that may involve a frequency division by an odd number. Frequency synthesis is an example. A frequency division by 3, 5, or 7, and so on, may be desired for generating a signal at a particular frequency, or for generating a signal having particular characteristics, or both. A controllable frequency divider, which is capable of providing closely spaced even and odd frequency division ratios, such as, for example, 2, 3, 4, 5, 6, and 7, may be used to advantage in a frequency synthesis system. Such a controllable frequency divider can provide an output signal that can be tuned over a relatively wide frequency range on the basis of an input signal that can be tuned over a relatively small frequency range only. Accordingly, it is possible to achieve a relatively wide tuning range, without this requiring an oscillator having a relatively wide tuning range.
Frequency division by an odd number can also used to advantage in radiofrequency systems that comprise a so-called harmonic rejection mixer. A harmonic rejection mixer effectively multiplies an input signal with a composite mixer driver signal, which is made up of individual square-wave-like signal components. The individual square-wave-like signal components have a particular magnitude, frequency, and phase relationship with respect to each other. This particular magnitude, frequency and phase relationship allows suppression of one or more of harmonic frequency components in the composite mixer driver signal, which would otherwise cause significant spurious responses. Achieving this particular frequency and phase relationship may involve at least one frequency division by an odd number.
In numerous applications, such as frequency synthesis and harmonic rejection mixing as discussed hereinbefore, it is desired that a frequency division by an odd number produces an output signal that has a 50% duty cycle. Such an output signal may also be in the form of a pair of signals, which have a 180° phase relationship. What matters is that the output signal comprises transitions that are equidistantly spaced in time. Such a 50% duty cycle signal allows generating precise in-phase and quadrature signals, in the sense that these signals have a precise 90° in phase relationship with respect to each other. In practice, an output signal will suffer from a duty cycle error: a deviation from the ideal of equidistantly spaced transitions. A duty cycle error, for example, will cause a phase error between the in-phase and quadrature signals, which will adversely affect signal processing quality. In a harmonic rejection mixer, a duty cycle error may adversely affect the suppression of one or more of harmonic frequency components.
International patent application published under number WO 2006/018754 describes a frequency-division circuit capable of providing a frequency division by an odd number and producing an output signal that has a small duty cycle error. The frequency-division circuit comprises a pair of multi-state circuits, each of which can be switched throughout a cycle of states. One multi-state circuit switches to a next state in response to a rising edge in an input signal. The other multi-state circuit switches to a next state in response to a falling edge in the input signal. Each multi-state circuit has at least one state in which the multi-state circuit inhibits the other multi-state circuit so as to prevent the other multi-state circuit from switching to the next state. Although the frequency-division circuit allows satisfactory signal processing quality, implementations are relatively costly because two multi-state circuits are required.